biggers front sprocket?

Newbie geezer here. I have a Hampton Cruiser, single speed.

Can bike shops put a larger front sprocket and matching chain on it for me to give me a little more "oomph" for pulling grades (feels like upslopes are all I have around this place, no matter which way I'm going)?

Wish I had some pics of me wobbling around our 'hood on that thing. I thought I could hop right on and ride like I did when I was a kid. I clearly recall how it felt. Problem being it doesn't feel the same way today. Not gonna be any trick riding or jumping for a bit!

My seat post doesn't go up high enough. Can bike shops get me a taller post?

I'm also going to need to raise the handlebars. I don't just mean tilt up, but getting the whole assembly up. Do the bike shops have parts for doing that?

My rear brake doesn't work.....well, it sort of doesn't work. I have to really chow down on the pedal in reverse, and then it coasts along not as fast as if I let up on the pressure. Is this something I can work on?

The mechanical forum would probably be more appropriate since those types of questions are not specific to the age of the rider. You also referenced LBS in several of your questions. Why not ask people at an LBS directly?

I larger front sproket will definitely not help you get up hills. A larger rear sproket might, don't know if you can change it. Lowering the weight of the bike and load will help.
You can probably buy a longer seat post.
You can probably have the handlebars raised, this may be a minor adjustment or it may require some extra parts, depending on what you have now.

A larger chainring is a move in the wrong direction-it will make your ratio HIGHER, rather than lower, which is what you need.
I don't know anything about a Hampton Cruiser, but I found a picture online, and it showed an Ashtabula (one-piece) crank. If yours has one, you'd have to find a whole new crankset that would fit and have a smaller ring, way more trouble and expense than it's worth.
You might be able to put on a larger rear sprocket fairly easily, though. I haven't worked on a coaster-brake bike since my kids were small, and my son's 25 now, so I don't remember how big a hassle it is to change cogs. If you can find a BMX-oriented shop (a real bike shop, not WalMart's bike department, that sells a lot of kids' bikes), they could tell you in five seconds and probably do the job in five minutes.

You asked: Can bike shops put a larger front sprocket and matching chain on it for me to give me a little more "oomph" for pulling grades

The answer is yes, but I think what you actually want is a SMALLER front sprocket? The ratio between the front and the rear determines your mechanical advantage (or "how hard it is to pedal"). The smaller the front, and the larger the rear, the easier your bike will be to pedal. If you're having problems ascending grades, you want the smaller front. If I've misunderstood your question, forgive me.

You asked: My seat post doesn't go up high enough. Can bike shops get me a taller post?

The answer again is yes - but... If your bike has the cheap 1" steel seat post (and most cruiser bikes do) and you weigh more than 200, raising the seat will only cause you to bend the seat post. I speak from experience! If this doesn't apply to you, congratulations! There's no good way that I know of to significantly raise the seat on a cruiser (although others may chime in on this..)

You asked: ...raise the handlebars...Do the bike shops have parts for doing that?

The answer is yes. You need a longer "stem." The stem is the thing that sticks up out of the frame and holds the handlebars. It is usually chrome on cruiser bikes. The stem you have may be able to come up some, but if you need lots of rise, a new stem will be needed.

You asked: My rear brake doesn't work...Is this something I can work on?

Probably not, unless you're good with tools & are willing to completely disassemble/reassemble your rear coaster brake. Not even bike shops want to work on coaster brakes - they usually replace them because of the cost of the time involved in repair. By the way - THIS IS A SAFETY ISSUE! Don't ride the bike until you get that brake fixed! We don't want to lose you.

Now for the kicker - You're looking at LOTS of work on this cruiser. Consider donating the bike to the Salvation Army, taking the tax deduction, and buying yourself a new bike. Even if you do all the work you need, you'll still have a Hampton Cruiser. If you plan to ride more than occasionally, go to the local bicycle shop (NOT the local discount store), and look at entry level "comfort" or "hybrid" bikes. The money you spend will provide you with the following benefits:

I'm with FarHorizon--sorry, I didn't read the whole post the first time and got fixated on the gearing issue. Coaster brakes are sort of interesting to take apart, but not nearly so much fun to put back together....
You probably could find a better bike in a thrift shop for less than $50, perhaps MUCH less. I recently bought my wife a Specialized HardRock (a medium cheap mountain bike from the early '90s) to ride in the rain, in very good shape, for $20. If you find something like that and don't want to fool with shifting, just put it in a gear you like and leave it there.